What are Degree of Freedom?
We have seen this curious expression in two setting now in the use of t-test and when using the Chi-squared test.What exactly are degrees of freedom,anyway? More specifically, let's look at to situations where these words come up.The expression
(where x mean is the average of the xs),is associated with N - 1 degree of freedom. Similarly,in a 2 * 2 table of counts,we always say the chi-squared statistic has one degree of freedom .The general rule is: Degree of freedom the number of data points to which you can assign any value.Let's see how to apply this rule, when we look at the expression sum(xi-mean x)^2, there are N terms in the sum. Each term is a squared difference between an observation x and the average x mean of all the xs. Let us look at these differences and write them down. We have d1=xi- mean x , d2=x2-mean x.........dN-mean x.